Решите уравнение в целых числах. xy=x+y+3

xy = x + y + 3
x(y - 1) - (y - 1) = 4
(x - 1)(y - 1) = 4
x - 1 = 1; y - 1 = 4 → x = 2, y = 5;
x - 1 = 4; y - 1 = 1 → x = 5, y = 2;
x - 1 = 2; y - 1 = 2 → x = 3, y = 3;
x - 1 = -1; y - 1 = -4 → x = 0, y = -3;
x - 1 = -4; y - 1 = -1 → x = -3, y = 0;
x - 1 = -2; y - 1 = -2 → x = -1, y = -1;